Investigating the effects of deforestation on water quality in the Wüstebach catchment, Germany

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MSc Earth Science

Environmental Management

Research Project

Investigating the effects of deforestation on water quality

in the Wüstebach catchment, Germany

by

Kerri-Leigh Robinson 11442034

October, 2020

ECTS Credits: 30

February 2020- December 2020

Assessor:

Examiner:

Prof. dr. Roland Bol

dr. Erik Cammeraat

Daily Supervisor:

Dr. Heye Bogena

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Declaration

By submitting this document electronically, I, Kerri-Leigh Robinson declare that the entirety of the work contained herein is my own, original work. I am the sole author thereof (save to the extent explicitly otherwise stated), that reproduction and publication thereof by Amsterdam University will not infringe any third-party rights and that I have not previously in its entirety or in part submitted it for obtaining any qualification.

Amsterdam, 24 December 2020

Kerri-Leigh Robinson

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Abstract

Deforestation has the ability to alter the natural biogeochemical cycling of elements and as a result this can impact nearby freshwater systems. Determining the effects of deforestation on water quality is beneficial in informing management and conservation efforts of disturbed catchment areas. This study assesses the impact of deforestation on water quality by evaluating the nutrient levels of dissolved organic carbon (DOC) and nitrate (!"_!!) in the Wüstebach headwater catchment in the North

Rhine-Westphalia state of Germany. This catchment area serves as an ideal research area as it forms part of the Terrestrial Environmental Observatories (TERENO) initiative, and it has therefore been equipped to monitor changes in the environment for over a decade. Additionally, there is a parallel catchment that serves as an unaffected reference catchment to the deforested catchment.

As well as analyzing DOC and !"!!, their relationship to runoff and soil water content (SWC) were

also analyzed in an effort to determine the effect of deforestation on DOC and !"!" export. The

methodology employed includes regular statistical analysis including, but not limited to, linear regression and Pearson’s correlation coefficient testing. In addition, a more advanced correlation analysis, namely wavelet analysis, was conducted in order to determine changes in the correlation and lag time between the variables of interest over different time scales.

This study found that following deforestation, there was an immediate increase in DOC and an increase in !"!" was only observed approximately one year following the deforestation. Elevated stream water

nutrient levels peaked around 2 to 3 years after the clear-cutting and returned to pre deforestation levels after approximately 5 years. The deforestation appeared to have no influence on the negative correlation between DOC and !"_!" as this remained negative with strong seasonal variation throughout the investigation period. The correlation between SWC/Q and DOC indicated that the negative correlation reduced following the deforestation and completely diminished approximately 3 years after the event whilst the negative correlation in the reference catchment remained stable. These findings have important implications for water catchment areas as they indicate that water quality may be affected for up to 5 years following clear-cutting. Forest management practices could focus on reducing nutrient export by the creation of buffer strips around catchment streams. Alternatively, to reduce deforestation disturbance, silvicultural management practices could be implemented when trying to return forest stands to their natural forest vegetation.

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Acknowledgements

I would like to express my deepest appreciation to Dr. Erik Cammeraat at the University of Amsterdam. Dr Cammeraat has supported me not only throughout this research project but also throughout my master’s degree. I am incredibly grateful for his advice and support throughout the past two years. I would also like to extend my deepest gratitude to Dr. Heye Bogena at the Jülich Forschungszentrum for sitting with me and teaching me about data preparation and wavelet analysis. Without his support, this analysis would not have been possible.

I’m also extremely grateful to my supervisor, Dr. Roland Bol, at the Jülich Forschungszentrum for his support with organizing the formalities of my stay in Jülich and assisting me to settle in. In addition to this, I am grateful for his support and feedback throughout the research period. Many thanks to Horst Hardelauf at the Jülich Forschungszentrum for teaching me to run the wavelet scripts in MATLAB and for providing assistance when necessary.

I would like to extend my sincere thanks to my uncle, Dr. Ashley Westaway, for proof-reading this paper at short notice and providing me with valuable feedback. I would also like to extend my thanks to Dr. Thomas Walmsley, for proof-reading earlier versions of this paper and supporting me throughout this degree. The encouragement that I have received from him and my aunt, Dr. Sally Walmsley, has been unmatched and I am incredibly grateful for their encouragement and guidance. I would also like to thank my mother for her support throughout my academic career, and for providing me with the opportunity to further my studies abroad.

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List of Abbreviations

AR1 – First Order Autoregressive Processes C – Carbon

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COI – Cone of Influence

DOC – Dissolved Organic Carbon EEA – European Environment Agency ET - Evapotranspiration

GPP – Gross Primary Production N – Nitrogen

NEE – Net Ecosystem Exchange NEP – Net Ecosystem Productivity NPP – Net Primary Productivity Pdf – Probability density function Q – Runoff

SWC – Soil Water Content

TERENO – Terrestrial Environmental Observatories W10 – Wüstebach Station 10 (Wu_010)

W14 – Wüstebach Station 14 (Wu_014) W17 – Wüstebach Station (Wu_017)

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List of Formula Symbols

!1/!2 Normalization constants &'_! Methane

&(_" Carbon dioxide &(_#"_ Carbonate ions &_% Non- &(_" exchange e Edge

) Evapotranspiration

)_' Transpiration Evaporation

)₍ Interception Evaporation '&(#− Bicarbonate ions

k Fourier frequency index + Leakage , Sample size - Dimensionless time ._" Nitrogen gas .'_# Ammonia .'!+ Ammonium .(_") Nitrite .(#) Nitrate 0 Precipitation 0_* Power Spectrum 0+, Throughfall 1_, Interflow 1_,, Surface runoff 2 Runoff 2_' Autotrophic respiration 2_- Heterotrophic respiration 2_. Recharge S Smoothing operator s Wavelet’s scale

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3₊₍₂₁ Smoothing in time 3_, Fast response reservoir 3( Interception reservoir

3₃₄ Root zone reservoir 3_. Slow response reservoir 35 Snow reservoir

t Time

4_0'67 Lag time from storm to peak flow

4_0'68 Lag time for rootzone recharge to enter groundwater

|69:_{| Cross wavelet power}

7; Dimensionless frequency x Value of x 8_< Time series x y Value of y 9_< Time series y := Confidence level

∆3 Change in groundwater storage ∆4 Time <0 Morlet wavelet >_>+ Fourier period ?@ Equidistant timesteps ∆7 Frequency ∑< (?@ Sample mean

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1. Introduction

Forest systems are important resources, providing many socio-economic functions and services to humans and ecosystems (Dessie & Bredemeier, 2013). Despite the importance of forests, the rate of deforestation is increasing globally, and this type of disturbance can have ripple effects on connected systems. According to Dessie & Bredemeier (2013), deforestation can alter the natural biogeochemical cycling of elements, and this can be seen by analyzing stream water runoff (Q) from catchments where forests have been cleared/harvested (Mupepele & Dormann, 2017). Since anthropogenic activities can alter water quality, it is important that these freshwater systems are appropriately managed and conserved (Bogena, et al., 2018). Biogeochemical cycling can be defined as the pathway by which a chemical element cycles through the biosphere, atmosphere, hydrosphere and the lithosphere (IPCC, 2014; National Science Foundation, 2009). Several biogeochemical cycles are operating at different levels at any moment in time in order to enable balance in the environment. Two of the most common biogeochemical cycles are the carbon (C) and nitrogen (N) cycles as they are tightly linked with one another due to the metabolic requirements of organisms for these two elements (Bala, et al., 2013; Kaplan & Newbold, 2000). Changes in N or C availability will not only influence the biological activity in an environment, but it will also influence the availability and requirements for the other element (Bala, et al., 2013). In the long term, the availability of these elements, or lack thereof, will affect the structure and performance of ecosystems.

When assessing the impact of deforestation on water quality in terms of the C and N cycles, it is useful to assess the forms of C & N that are soluble upon contact with water and are necessary

for marine ecosystem functioning. Nitrates (.(#)) and Dissolved Organic Carbon (DOC) are

highly soluble forms of N and C and thus they move readily from the terrestrial environment to the marine system when saturated (WHO, 2011). Although other forms of C are soluble, DOC comprises the largest pool of organic C in marine environments and it serves as a vector for the transport of nutrients to microorganisms within water bodies (Mostovaya, et al., 2017). According to published literature on the influence of deforestation on Q generation, deforestation events have the potential to increase the Q and sediment yields from the catchment area (Gholami, 2013; Hlásny, et al., 2015). Therefore it can be inferred that nutrient levels in catchment streams will be altered by the increased Q and sediment yields.

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When assessing literature on studies focused on the effects of deforestation on .(_#) content

in temperate streams it is found that .(_#)content increases (Malek & Krakowian, 2012) and

this increase can continue for up to five years after the deforestation event (Mupepele & Dormann, 2017). Through examining studies that assessed the effects of deforestation on both DOC and N content it is suggested that both DOC & N content increase in streams affected by deforestation (Gandois, et al., 2012; Jacobs, et al., 2017). However Gandois et al. (2012) suggested that the rise in DOC may have more to do with catchment characteristics than land-use changes. It should be noted that both of these studies were conducted in tropical regions; the results for temperate regions may be different. Therefore, investigating the effects of deforestation on the C & N cycle in temperate regions is useful in filling a knowledge gap and informing conservation and management efforts for these regions.

A suitable research site for the investigation of deforestation on water quality would be one in which water quality and composition has been monitored for a long period of time. Ideally this water quality and composition monitoring would be assessed at regular intervals for the entire timeframe from pre-deforestation to a few years after the deforestation event. Analyzing this data would give a holistic representation of stream changes due to deforestation. The TERrestrial EnviroNmental Observatories (TERENO) initiative has various research sites situated around Germany which have been equipped to measure changes in the environment (Zacharias, et al., 2011). One of the TERENO observation sites known as Wüstebach research site has been purpose-built in order to investigate the effects of deforestation on the ecosystem, hydrology and biogeochemical processes (Umweltbundesamt GmbH, 2020b). This serves as an ideal research site as Q data, water quality data and water composition data exist for the entire timeframe spanning pre-deforestation to post-deforestation.

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2. Research Aim

The main objective of this paper is to assess the impact of deforestation on the water quality of streams in the Wüstebach catchment. The solutes evaluated in this study include DOC and .(#) as these have the potential to alter water quality. Assessing how deforestation alters the

concentration and relationship between different solutes could assist in making future projections about the influence of deforestation on water quality and inform land management practices.

2.1. Research Questions

1. Has the deforestation event altered the in-stream DOC and .(_#) concentration in the

Wüstebach catchment?

2. Did the deforestation affect the correlation between in-stream DOC and .(#)?

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3. Site Description

The TERENO Wüstebach research site was established in 2004 and it was equipped with various measurement instruments between 2007 and 2010 which allow the long-term monitoring of the environment (Bogena, et al., 2015). The site forms part of the larger Eifel/Lower Rhine Valley observatory and it is monitored by the Jülich Forschungszentrum. The purpose of this research site is to investigate the consequences of deforestation on hydrological processes, the ecosystem and biogeochemical cycles using an integrated observation approach (Umweltbundesamt GmbH, 2020b).

3.1. Location and Characteristics

The TERENO Wüstebach catchment is located in the southern part of the Eifel/Lower Rhine Valley Observatory. It falls within the Eifel National Park and it is in close proximity to the

German-Belgian border located at 50°30A_{16 N and 6°20" ) (6H3 84). The site covers an area}

of 38.5 ha and sits at an average attitude of 610 meters above sea level. The catchment is characterized by small headwater streams that receive an annual precipitation of approximately 1220 mm per annum. This is shown in Figure 1 below. The Wüstebach catchment and the Püngelbach catchment combine to form the headwater of the Erkensruhr River. North east of the catchment is the reference stream which is also instrumented to serve as a comparison for the Wüstebach stream. The reference stream has a size of 11 ha and feeds into the Wüstebach stream approximately 10 m downstream. This alliance can be seen in Figure 1.

3.2. Vegetation and Deforestation

Norway Spruce (Piceas abies) is the dominant vegetation found in the catchment as this species was planted in 1946 for timber production. However, efforts are currently being made to restore the Eifel National Park to near natural deciduous forest (Umweltbundesamt GmbH, 2020b). These efforts have included the clear-cutting of an area of 9ha within the Wüstebach research site. This deforestation was undertaken by the National Park Forest Management and it occurred in the late summer/early autumn of 2013. The extent of the deforestation event can be seen in Figure 1. Significant effects are expected in water quality as a result of the deforestation event. The reference site which is located North East to the catchment is an unaffected reference site that has not been subjected to deforestation. Using the reference stream, comparisons can be made between water quality in the deforested stream and the reference stream.

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3.3. Pedology and Geology

The bedrock of this catchment is comprised of weathered Devonian foliated siltstone and claystone and it contains isolated quartzite (Schuster, 2010). This layer is covered by a periglacial solifluction layer which ranges from approximately 1 to 2 meters in thickness. The pedology in this region can be seen in Figure 1 above. This figure indicates that the hill slopes are dominated by Cambisols and Planosols whilst the valley is dominated by Gleysols and Histosols. The dominant soil texture in this catchment is silty clay loam and the overlying litter layer ranges from 0.5 to 14 cm across the catchment (Umweltbundesamt GmbH, 2020b).

3.4. Site Instrumentation

As mentioned above, the Wüstebach research site was equipped with monitoring instrumentation between 2007 and 2010. Thus, environmental measurements were taken long before the deforestation occurred. In order to create an integrated observation system, the site was equipped to measure the following parameters: runoff, groundwater and water quality; meteorology; soil moisture; water balance; sap flow; isotope monitoring; soil respiration; and soil properties (Bogena, et al., 2015). The instrumentation used to measure these parameters relevant to this study will now be discussed. For more detailed information on the instrumentation in the Wüstebach catchment please see Appendix 1.

Figure 1: Map indicating the soil types and instrumentation of the Wüstebach catchment and the reference catchment as well as the extent of the deforestation (Bogena, et al., 2018)

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Three runoff gauging stations have been installed in the research site to measure stream discharge and these can be seen in Figure 1. In an effort to assess water quality, weekly grab samples are taken for chemical analyses at several locations along the Wüstebach stream (Bogena, et al., 2015). In addition to these locations, weekly grab samples are also taken from the main tributaries of the stream and the reference stream (runoff sampling stations in Figure 1). The parameters measured in these weekly samples include &L)_{, .M}B_, NL)_,3(

""), OB, .(#),

.'_!B_{, PQ}"B /#B_{, R,}"B_{, RS}"B_{, &M}"B_{, DOC, TN and TC. In addition to these concentrations,}

other measurements include water temperature, electrical conductivity, pH and redox potential. Soil moisture monitoring is done through the wireless soil moisture sensor network SoilNet (Bogena, et al., 2015). 150 sensor units have been placed in the catchment. These provide soil information wirelessly via several router devices to a central network coordinator unit (Bogena, et al., 2015). Water balance is assessed through six lysimeters installed in the catchment (Bogena, et al., 2015). These instruments also gather data on precipitation, evapotranspiration, and changes in soil water storage.

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4. Theoretical Framework

This section reviews existing literature about hydrological and biogeochemical processes occurring at the catchment scale. This chapter will begin by describing the hydrological cycle at catchment scale, followed by the carbon and nitrogen cycles and it will conclude by evaluating existing literature on the effect that deforestation has on these catchment processes.

4.1. Hydrological Processes at the Catchment Scale

A catchment area has been defined by the EEA (2020) as a land area from which surface runoff is transported by a single drainage system into a river, basin or reservoir. An overview of the hydrological processes occurring at the drainage basin level can be seen in Figure 2.

Water enters the catchment through precipitation in both solid (hail and snow) and liquid forms (drizzle and rainfall) (Ward & Robinson, 2000). This precipitation can either fall directly into the catchment channel, termed channel precipitation, or onto the land and intercepted by the vegetation. A portion of the water intercepted by the vegetation may be evaporated before it takes part in the land-bound hydrological cycle. The portion of water that is evaporated is

dependent upon land cover

characteristics, rainfall characteristics, and on evaporative demand (Gerrits, 2010). The remainder of the water will reach the land surface through throughfall and it will either infiltrate into the soil water or it will enter the channel storage through overland flow termed surface runoff.

The vegetation extracts a portion of soil water through the process of osmosis and that water is then evaporated through transpiration (Ward & Robinson, 2000). The remaining soil water will

lnterc eption VEGETATION Stemflow and throughfall SURFACE PRECIPITATION Channel precipitation

i---- Overland flow - - . i

Floods -...JW We, Z<: za: Capillary Infiltration <o I1--UW rise

,_ ---- _{SOIL WATER} Throughflow --.,~ ... _,...

Evaporation Transpiration Capillary rise I -- --~ . Percolation Baseflow GROUNDWATER - - Recharge l . . . - - - ' RUNOFF

Figure 2: Overview of the hydrological system at the drainage basin level (Ward & Robinson, 2000)

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then either enter the channel storage through throughflow or it will percolate into the groundwater table where it recharges the groundwater. A fraction of channel storage water is lost to evaporation and groundwater recharge and the remainder is transported out of the catchment through Q.

The water balance equation describes the flow of water moving in and out of a system. This equation is defined as follows:

Equation 4.1

∆3

∆@ = 0 − ) − 2 − +

Where ∆3 is the change in groundwater storage for the water-balance period ∆@. It is calculated by subtracting evapotranspiration (E), Q from the catchment exit (R), and groundwater leakage (L) from the precipitation (P) (Hossain, et al., 2015). As water is an excellent solvent, it acts as a transport medium for ionic and polar compounds (Fairbridge, et al., 1998). Therefore, changes to hydrological processes can have an impact on the biogeochemical cycling occurring at catchment scale.

4.2. The Carbon Cycle

C is the fourth most abundant element in the universe, and it is an essential element to all life on earth (Reynolds, 2012; Riebeek, 2011). All living organisms are formed from organic molecules that contain C and the availability of this element is made possible by the C cycle. The global C cycle can be viewed as a series of reservoirs of C in the earth system which are linked by exchange fluxes (Bala, et al., 2013). Forest ecosystems are one of the largest reservoirs of carbon and hence the flux of carbon inside these systems has a large impact on the global C cycle (Melanidis, 2017). The C cycle occurring at the forested ecosystem scale can be seen in Figure 3.

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Figure 3: The C cycle in a forested ecosystem indicating the main fluxes and neglecting minor pathways such as flowers, fruits and paths. Solid arrows indicate C fluxes, grey arrows indicate nutrient fluxes, and the broken line indicates a major feedback of C allocation (Schulze, 2000).

The C cycle starts with the assimilation, also known as fixation, of &(_" by vegetation and this process is rapid and dependent on light energy (Schulze, 2000). This assimilated &(" , known

as gross primary production (GPP), is converted to organic compounds and it is used for vegetation growth, defense or reserve (Loustau & Rambal, 2010). Figure 4 outlines the net ecosystem changes occurring in the forest carbon cycle. &(" is returned to the atmosphere

through plant respiration (2_') and the difference between assimilation and &(_" respiration

coupled with non- &(" exchange

(methane (&'_!) or isoprene), represented as &_%, is known as net primary productivity (NPP) (Schulze, 2000; Loustau & Rambal, 2010). NPP can thus be described as the net carbon uptake by the vegetation (Loustau & Rambal, 2010). &% is a marginal flux in well-drained forest

ecosystems when normal conditions are occurring.

Figure 4: The forest carbon cycle showing net ecosystem change (Loustau & Rambal, 2010)

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The loss of vegetation due to litterfall and decay feeds back into the ecosystems by supplying organic matter to the heterotrophs that use the stored energy to recycle nutrients supporting future plant growth (Schulze, 2000). These heterotrophs decompose the organic matter and as a result they release &(_" through respiration back into the atmosphere, assimilation minus

heterotrophic respiration (2_-), and autotrophic respiration (2_') yields net ecosystem exchange

(NEE). The change in C storage of the forest ecosystem, including growth and soil C, is therefore quantified by NEE (Schulze, 2000).

C is additionally exported out of the forest ecosystem mostly by biological beings such as herbivores during migration and humans harvesting areas of the forest ecosystem (Loustau & Rambal, 2010). A smaller fraction of carbon is exported through wind, flooding or fire. The dissolved carbon flow represents the portion of dissolved organic and inorganic carbon leaving the forest ecosystem and it can account for a significant percentage of the forest ecosystem carbon balance (Loustau & Rambal, 2010). Dissolved inorganic C consists of dissolved &(_" and bicarbonate ('&(_#−) and carbonate ions (&(_#"_) (Post, et al. , 1990). DOC consists of both large and small organic molecules. Particulate organic C is comprised of organic molecules that are larger than 0.7 micrometers such as live organisms and fragments of decaying plant/animal material (Post, et al., 1990; Zhuiykov, 2014). Quantitatively, DOC is the largest pool of organic C in marine environments and it is a vector of energy and nutrients from terrestrial to aquatic systems for heterotrophic organisms (Mostovaya, et al., 2017).

4.2.1. DOC and Stream Water

DOC can be defined as the organic matter dissolved in water that is capable of passing through a filter that removes material between 0.22 and 0.7 micrometers (Zhuiykov, 2014). Organic C is formed as a result of decomposition of plant or animal material and this C may partially dissolve upon contact with water. A fraction of organic C in rivers originates from the internal productivity of the water and the majority is leached from terrestrial landscape (Schlesinger & Berhardt, 2013). DOC that originates within the internal environment is termed autochthonous DOC and it is formed from the decayed remains of aquatic organisms and precipitates (Matthews, 2013). Allochthonous DOC originates from the terrestrial environment (Matthews, 2013; Schlesinger & Berhardt, 2013). When DOC is transported through the river system, the aquatic microbes assimilate and respire most allochthonous DOC and therefore practically no terrestrial DOC reaches the ocean (Schlesinger & Berhardt, 2013).

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The carbon budget of most small streams is dominated by particulate carbon (Schlesinger & Berhardt, 2013). Various forms of plant material fall into streams and are subsequently shredded and decomposed during transport. The resultant particulate matter supports diverse aquatic food webs (Schlesinger & Berhardt, 2013). As stream size increases, the ratio of dissolved to particulate terrestrial carbon inputs increases due to the degradation of particulate matter and the smaller portion of terrestrial bank from which to attain particulate matter (Webster & Meyer, 1997; Schlesinger & Berhardt, 2013). As channel size increases further, autochthonous production from benthic algae and macrophytes becomes increasingly significant. Therefore, increases in ecosystem productivity are expected along the river continuum (Schlesinger & Berhardt, 2013).

Carbon can also enter streams already in the form of DOC and this occurs when water originates from areas with a high proportion of organic soils, this organic matter can drain into rivers and lakes and end up in aquatic systems. Due to the particle size of DOC, it is typically transported via surface runoff to nearby water sources (Hau, et al., 2014; Neu, et al., 2016). According to Kaplan & Newbold (2000), DOC concentrations in streams and rivers, under baseflow conditions, can range from < 0.5 `S&+)@_{in alpine and everygreen forests to}_>

30 `S&+)@_{where streams and rivers drain wetland areas. Factors that influence the}

concentration of DOC in water sources include catchment vegetation; climate; microbial activity; soils and hydrology (Kaplan & Newbold, 2000). Since DOC is an important food source for marine microorganisms and is necessary to ensure ecosystem health, it is important for DOC concentrations in a water body to be above a certain level depending on ecosystem requirements. When assessing DOC content with respect to drinking water quality, water with high levels of DOC is a cause for concern (Ledesma, et al., 2012). This is because DOC can act as a vector for other contaminants, such as pesticides and heavy metals, from the terrestrial environment and this, in turn, increases the cost of the drinking water treatment process (Ledesma, et al., 2012; Hau, et al., 2014).

4.3. The Nitrogen Cycle

N is the 4th_{most plentiful element in cellular biomass, and it forms the majority of the earth’s}

atmosphere (Ngatia, et al., 2018; Stein & Klotz, 2016). N is an essential element of amino acids which are the building blocks of proteins and thus it is a vital element for all living beings

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(Stein & Klotz, 2016). Despite the vast abundance of N in the atmosphere, absorption into organisms is challenging. For autotrophs to receive N, they require symbiotic bacteria to perform biochemical processes termed fixation, nitrification, ammonification/mineralization, and denitrification (Stein & Klotz, 2016). An overview of the N cycle at forested catchment scale can be seen in Figure 5. N assimilation is the first step of the biological N cycle and it includes the conversion of atmospheric N (._") into a usable form through assimilation, oxidation by electrical discharge or combustion processes (Schulze, 2000; Zhu, et al., 2015).

Biological N fixation is the most common form of fixation and it occurs when ._" is deposited

into the soil. Once deposited into the soil, the ." undergoes changes as a result of the soil

bacteria. The soil bacteria separate the two N atoms and enable them to combine with hydrogen

to form ammonia (.'_#) and then ammonium (.'_!+).

.'_!+ is then converted to nitrite (.(_")) and nitrate (.(_#)) by further microbial processes in the soil. This process is very important as plants are incapable of absorbing ammonia. The

process of converting ammonia to .(_#)_{is termed nitrification.}_.(

#) are then taken up by

primary producers during their growth and it is used in the production of organic nitrogenous compounds in the process of assimilation (WHO, 2011). Decaying plants and animals feed back into the N cycle as the organic N is released back into the soil. The conversion of organic N to ammonium is termed ammonification/mineralization (University of Hawaii, 2007).

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Conditions that affect N mineralization include the quantity of organic N; temperature; oxygen; moisture content; and the ratio of carbon to nitrogen (C: N) of the decomposing organic matter (University of Hawaii, 2007). According to the University of Hawaii (2007), microorganisms in the soil need both C and N to mineralize and net mineralization occurs when the ration is less than 20:1.

Immobilization is the reverse reaction of mineralization and it occurs when decaying organic matter is low in N and therefore has a high C to N ratio (University of Hawaii, 2007).

Denitrification is the final stage of the N cycle and it involves the conversion of .(#) into

gaseous N (._") (Stein & Klotz, 2016) through microbial processes and it occurs through the removal of oxygen (Ngatia, et al., 2018). According to OECD (2018), total denitrification is influenced by the available oxygen, organic C and pH of the soil. This process thus returns N from the biosphere to the atmosphere (OECD, 2018) and closes the cycle.

4.3.1. .(_#) and Stream Water

Anthropogenic activities have the potential to alter the N cycle and affect the quantity of ions found in different parts of the cycles (Schlesinger & Berhardt, 2013). Activities that are known to alter the N cycle include: the combustion of fossil fuels and biomass (Zhu, et al., 2015); N-fixing plants cultivation (Zhu, et al., 2015); the application of artificial N fertilizers to increase crop production; and clearing vegetation which results in increased mineralization and

therefore a buildup of .(_#) in the soil (Rusinga, et al., 2008). This is owed to the fact that

decaying vegetation that is rich in N will release N back into the soil, and due to the lack of bacteria present in the soil, this N will be in excess of soil biota requirements leading to N loss through leaching or nitrous oxide emissions (Zhu, et al., 2015) (Rusinga, et al., 2008). In this

way, .(_#) can potentially leach into groundwater or be carried away by surface Q to nearby

water bodies (Zhu, et al., 2015). It is therefore clear that vegetation clearing/deforestation can

alter the N cycle by producing large amounts of mobile .(_#)_.

Water pollution caused by N can impact both the ecosystem as well as animal and human health (OECD, 2018). Excessive levels of N in water bodies cause eutrophication which in turn can lead to anoxic events (Ngatia, et al., 2018). Eutrophication occurs when a body of water contains a high level of nutrients, often due to run-off from the land, and these nutrients promote excessive growth of plant life and algae blooms (Ngatia, et al., 2018; OECD, 2018).

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Excessive growth of plants and algae can block the passage of light into deeper waters (OECD, 2018) .When these plants die and decompose, oxygen is removed from the water resulting in an anoxic event which is often deadly for other marine life as it deprives them of oxygen. High concentrations of .(_#)_{in drinking water can also cause Methemoglobinemia in infants}

(OECD, 2018) and according to Schullehner, et al. (2018), high .(_#) content in drinking

water may increase the risk of colorectal cancer in humans. 4.4. Nutrient Spiraling

The theory commonly used to explain nutrient cycling in streams is the notion of nutrient spiraling which implies that lotic nutrient cycles are continually relocated downstream by adjective flow (Schlesinger & Berhardt, 2013; Newbold, 1992). As the dissolved nutrients move downstream, they are accumulated by organisms in the stream and converted to organic forms. Once these organisms die, the nutrients are degraded, and the inorganic form is returned to the stream water and the process is repeated as the nutrient atom is exported out of the river system. An overview of the path that the nutrient takes is outlined in Figure 6. The wavy black line illustrates the path that the nutrient takes when moving downstream prior to sediment uptake (U) and then it is further transported prior to remineralization (R) followed by a release to the water column. The spiral length (S) of the nutrient molecule is therefore calculated by

combining the transport distance prior to removal of the water column (the uptake length (3₅))

and the distance transported within benthic sediments or biota (remineralization length (3_D))

(Schlesinger & Berhardt, 2013).

Figure 6: Stream nutrient spiraling adapted by Schlesinger & Berhardt, (2013) (Newbold, 1992).

Typically, .(_#) in stream water has a longer uptake length than alternative forms of N such

as .'_!+ (Schlesinger & Berhardt, 2013). This difference is due to preferential uptake of

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portion of .'_!+ that enters the stream water is immediately nitrified and as a result increasing .(_#) concentrations. This process facilitates the downstream transport of N in .(_#)form which contributes to N pollutant loading (Bernhardt & Likens, 2002). As .(#) is poorly

absorbed, .(_#)spiraling is almost wholly controlled by biological processes (Schlesinger &

Berhardt, 2013). Commonly, .(_#) stream uptake rates increase with loading however high

loading rates can easily saturate this capacity (Mulholland, et al., 2008).

4.5. Temporal Dynamics and Periodicities at Catchment Scale

Changes in C availability and processing are good correlates of N within streams. This is due to the stoichiometric and thermodynamic constraints of organisms and this correlation has been illustrated in experiments where labile C has been added to stream sediment samples and the result has been a decrease in nitrification (Schlesinger & Berhardt, 2013; Strauss, et al., 2002; Strauss & Lamberti, 2000). This is because organic carbon fuels assimilation and

denitrification. Therefore, under typical conditions, in-stream DOC and .(_#)_{content have a}

negative correlation as biological capacity for .(_#) uptake is limited by labile C (Bernhardt

& Likens, 2002).

A previous study conducted on the study site, prior to the deforestation, assessed the temporal and spatial changes in .(_#) and DOC in the catchment streams (Weigand, et al., 2017) .

Weigand, et al. (2017) did not observe long-term trends between DOC and .(#) in the surface

water however they did find strong seasonal variation with high DOC concentrations occuring

in the summer and high .(_#)_{concentrations occuring in the winter. This finding is in line with}

the observations of a number of studies (Piatek, et al., 2009; Taylor & Townsend, 2000;

Williams, et al., 2011). Additionally, they found that the DOC, .(_#) and ratio of the solutes

in the Wüstebach streams was mainly controlled by hydrological mixing processes and whilst in the soil, the solutes were controlled by biogeochemical cycles (Weigand, et al., 2017). This finding suggests that the solute ratio is a robust indicator for water pathways in the catchment. Conducting a follow-up study to determine the impact of deforestation on these nutrients is consequently beneficial as there is a current drive in many European countries to return forest stands to the natural forest vegetation (Bredemeier, et al., 2012). This process will involve replacing monospecific, ‘artificial’ conifer plantations with broadleaved mixed stands often via clear-cutting. These anthropogenic activities can lead to abrupt, immediate changes in forest

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ecosystems altering the carbon flux and stocks (Loustau & Rambal, 2010) and altering the N cycle by producing excessive mobile .(_#) that then has the potential to leach into water resources (Rusinga, et al., 2008). These effects are not only immediate, but they can also have delayed effects that alter the ecosystem for years (Loustau & Rambal, 2010). Anthropogenic activities thus have the ability to alter these nutrient cycles and could potentially alter their relationship with one another.

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5. Methods

5.1. Data Acquisition

As previously described, the Jülich Forschungszentrum is responsible for the Wüstebach catchment area and has been instrumenting and collecting data on this area since 2007. This

data is analyzed and published on a public online portal commonly referred to as TEODOOR.

The majority of the data used in this thesis was acquired from the online portal and a summary of the used datasets can be seen in Table 1 below. The only data set that was not accessible on

TEODOOR was the precipitation data that was acquired from the Deutscher Wetterdienst

website.

In order to determine the effects of deforestation on .(_#) and DOC concentration in the catchment, the results of weekly sampling campaigns at three sampling points were taken. These points, termed W10, W14 and W17, can be seen in Figure 7. W10 and W14 fall within the stream affected by deforestation and W17 is located in the reference stream that remained unaffected. The weekly sampling campaigns usually take place at the start of the week and they are conducted by the staff of the Jülich Forschungszentrum. The weekly samples are taken in glass bottles that are pre-rinsed in stream water prior to sample taking. The samples are then sealed and transported to the Forschungszentrum for lab analysis where the concentration of

DOC and .(#)are determined. The samples are kept at a temperature of 4℃ during transport

and storage at the Forschungszentrum and the samples are analyzed for DOC and .(_#)

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The TriOs sensor is installed at W14 and it

automatically measures .(_#) data in 15-minute

intervals. TriOs sensor .(_#) data was used to gap

fill the missing .(#) weekly sample data.

Discharge is also automatically measured at all three runoff stations in 10-minute intervals and discharge from the Erkensruhr Q station is automatically measured in 15-minute intervals. The Erkensruhr Q data was used to fill the discharge data from the three runoff stations. The soil water content (SWC) and Q data was used to determine if the deforestation event altered the processes leading to solute export. SWC data is measured by 150 SoilNet sensors in the catchment and the average of the clear-cut area (SWC_Mean_CC) is used for the

deforested catchment whilst the forested SWC (SWC_Forest) is used for the reference catchment. Daily evapotranspiration (ET) data and precipitation data was also gathered to

determine the correlation with DOC & .(#); however there was no noteworthy results drawn

from this analysis. The wavelet analysis results can be found in Appendix 5.3 and 5.4.

5.2. Descriptive Statistics

Following data acquisition, descriptive statistics were generated for Q, .(_#), DOC, ET, precipitation and SWC from all three stations. The quantitative statistics generated are useful in describing the basic features of the data. For the purpose of this study, a total of 522 weeks

were examined spanning the 4th_{of January 2010 to the 30}th_{of December 2019. The descriptive}

statistics for the different datasets are presented in Table 2.

Figure 7: Outline map of the Wüstebach catchment and the location of the sampling stations used in this project. Adapted from Weigand (2014).

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A complete data set for the full time period would have a total of 1566 data points per runoff station equating to a grand total of 4698 data points. 508 data points are missing from the data set and consequently there is 10.81% data missing. This missing data was gap filled prior to the wavelet analysis as wavelet analysis requires a complete, equidistant dataset to generate accurate results.

5.3. Descriptive Time Series

Time series graphs were created for all the variables at different stations in an effort to adequately visualize the solute trends over the investigation period. Time series analysis concerns time series data and it is a statistical technique that is useful in understanding trends in the dataset over the period of analysis. An example of a descriptive time series can be seen in Figure 8 below.

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This graph plots the concentration of DOC in the Wüstebach catchment stream (W14) and the reference catchment stream (W17) from the beginning of 2010 to the start of 2015. The time series indicates that the respective concentrations of DOC in the two catchments were closely aligned prior to June 2013. It is evident that after this date, the concentration of DOC in W14 increases whilst the reference stream remains stable. This increase in concentration can be attributed to the deforestation that only affected the Wüstebach catchment stream. This graph also indicates seasonal variations in DOC concentration in the catchment. One can deduce that higher concentrations of DOC are evident during the warmer months from May to October and lower concentrations are found in the colder months from November to April. In this way it is clear that time series graphs are useful in detecting sudden changes in the data set and seasonal/annual trends.

5.4. Boxplots

Box and whisker plots were made for all variables for each sampling station. These plots are a useful way of summarizing a set of data based on a five-number summary, namely: the minimum, lower quartile (Q1), median, upper quartile (Q3), and the maximum (Galarnyk, 2018). The box thus depicts the shape of the distribution, the central value, and the variability of the data set. An example of how to interpret a box plot can be seen in Figure 9.

0 2 4 6 8 10 12 14 01/01/ 2010 01/01/ 2011 01/01/ 2012 01/01/ 2013 01/01/ 2014 Co nc en tr at io n [m g/ l]

DOC concentration in W14 & W17 from Jan 2010 to Dec 2014

Deforestation DOC_W14 DOC_W17

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The colour box represents the interquartile range (IQR) and it represents 50% of the data points and it limited by the boundary of the lower (Q1) and upper quartile (Q3). The box plot is intersected by a black line indicating the median value of the dataset. Black lines extend from the box plot and these are commonly known as the ‘whiskers’, the whiskers extend to the maximum and minimum values which are calculated by multiplying the IQR by 1.5 and adding or subtracting that from the nearest quartile. The minimum value is therefore calculated using the formula 11 − 1.5 ∗ d12, and the maximum value is calculated using 13 + 1.5 ∗ d12. The outliers are plotted as individual points and symbolized with ‘e’ and they are data points that are not larger or smaller than three interquartile from Q1 and Q3. Once the data points exceed that range, they are termed extreme values and they are symbolized as ‘⋆’.

5.5. Regression Analysis

Regression analysis was conducted by creating scatterplots of the variables of interest and applying lines of best fit to determine the coefficient of determination (2"_{). Scatterplots were}

created to determine the trends in the relationship between DOC and .(#), Q and DOC, Q

and .(_#)_{, SWC and DOC, and SWC and .(}

#). A basic formula for the line of best fit with

two independent variables is as follows (Chen, 2020):

Equation 5.1

9 = ! + g_@(8_@) + g_"(8_")

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9 = hQiQ,hQ,@ jMklMgLQ ! = !m,n@M,@ g@ = 1n@ kQSkQnnlm, !mQool!lQ,@ g_" = 2,h kQSkQnnlm, !mQool!lQ,@ 8_@ = 1n@ l,hQiQ,hQ,@ jMklMgLQ 8" = 2,h l,hQiQ,hQ,@ jMklMgLQ

Once the line of best fit is applied, the 2"_{value can be calculated. The 2}"_{is a measure that}

determines the ability of a model to explain a result in linear regression and it is defined as follows (Enders, 2020): Equation 5.2 2@ _{= 1 −}233 433 233 = np` mo nqpMkQn mo kQnlhpMLn 433 = @m@ML np` mo nqpMkQn

The closer the 2"_{value is to 1, the stronger the relationship, and the closer the 2}"_{value is to}

0, the weaker the relationship is. The lines applied in this research include linear, exponential, logarithmic, and polynomial trendlines. An example of a scatter plot created for this research project can be seen in Figure 10. This plot indicates a negative regression between DOC and

.(#) for W17 over the investigation period. Four trendlines were applied to the scatterplot in

order to determine the line of best fit, which in this case is the polynomial trendline as it has

the highest 2"_{value of 0,5006. This indicates that 50% of the variation in the outcome has}

been explained just by predicting the result using the covariates in the model.

Figure 10: Scatter plot indicating the relationship between DOC & !"!" at sample station W17

R² = 0,3325 R² = 0,2791 R² = 0,4528 R² = 0,5006 -2 0 2 4 6 8 10 12 0 2 4 6 8 10 N itr at e [ m g/ l] DOC [mg/l] W17

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5.6. Correlation Analysis

A Pearson’s correlation coefficient test was conducted on the variables of interest to determine the linear correlation between the two variables. A correlation is a single digit that defines the degree of relationship between two variables (Trochim, 2020). Pearson’s sample correlation coefficient is defined by Field (2013) as:

Equation 5.3 k%E = ∑< (8₍ − 8̅ (?@ )(9( − 9s) t∑< (8₍− 8̅)" ()@ t∑<()@(9( − 9s)" 8₍; 9₍ = nMìLQ iml,@n 8̅; 9s = ∑< = (?@ @ℎQ nMìLQ `QM,. , = nMìLQ nlwQ

This coefficient returns a value, known as r, between -1 and +1 where -1 indicated a total negative correlation, +1 indicates a total positive correlation and 0 is indicative of no linear correlation. The strength of a correlation can also be determined from the r value where 0,1 < | r | < 0,3 indicates a small/weak correlation, 0,3 < | r | < 0,5 implies a medium/moderate correlation, and 0,5 < | r | infers a large/strong correlation between the variables of interest (Field, 2013).

5.7. Data Preparation

Prior to conducting the wavelet analysis, the gaps in the dataset were filled because this analysis requires a complete, consistent dataset to generate results. As stated in section 5.2, there was a total of 10.81% of data missing. Different methods were used to gap fill this missing data and they will now be explained.

5.7.1. .(_#) Filling

From the .(#) data there was a total of 191 points missing. To gap fill the missing data from

W14, TriOs sensor data was used when possible. The TriOs sensor is an automatic measuring device that is installed in W14. This sensor was installed in October of 2013 and it

automatically measures .(#) [mg/l] and SAK 254 [1/m] data in 15-minute intervals. These

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sample .(_#) data. A linear regression graph indicating the relation between the two variables can be seen in Figure 11 and a descriptive time series for 2014 can be seen in Figure 12.

Figure 12: Linear graph indicating the similarity between the !"!" concentration measured in the weekly samples and the TriOs sensor

Due to the strong positive correlation of the readings, the TriOs sensor data was used to gap fill the missing weekly sample data when TriOs sensor data was available. A line of regression was calculated using a total of 20 points, and the equation was used to calculate the missing data point. The TriOs sensor data was not available for the full time period as there were times when it was broken and recording inaccurate results. A total of 41 data points from W14 were filled using the sensor data and the remaining 21 data points were filled using linear interpolation methods. The missing data from W10 and W17 were filled by conducting

Figure 11: Scatter plot indicating a strong positive correlation between the weekly sample !"!" data and the measured TriOs sensor !"!" data.

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regression analysis with the complete W14 dataset using a total of 20 points, preferably 10 points before and 10 points after the missing value.

5.7.2. DOC Filling

The DOC data has a total of 193 data points missing. 61 of these points were missing from W14 and they were filled using linear interpolation. The remaining missing points from W10 and W17 were filled using regression analysis with the complete W14 data set. A line of

regression was determined using the same methods described for the .(#) gap filling.

5.7.3. Q Filling

The Q data was gap filled using linear regression and correlation with the Q data measured at the Erkensruhr gauging station. Due to the high resolution of the Q data, the data from all four Q stations (W14, W10, W17 and Erkensruhr) were first converted into daily averages. W14 was then filled using linear regression if there were <=5 points missing, if there were more than 5 points missing, these points were filled using regression analysis with Erkensruhr data using 10 points before and 10 points after the missing data were possible. The missing data from W10 and W17 were filled in the same manner using the filled W14 data. Once all Q data was filled for all three stations, the Q data taken on the dates of the weekly sample campaigns was extracted so that there was a complete, equidistant dataset available for the wavelet analysis.

5.8. Wavelet Analysis

Wavelet analysis is a multi-resolution analysis that has become a popular tool for analyzing localized variations of power within a time series as it breaks down a time series into time-frequency space (Torrence & Compo, 1998; Rathinsamy, et al., 2017). It is a useful tool in that it accounts for lagging effects in addition to altered strengths and signs of correlation at different time scales (Weigand, et al., 2017). In this way, it can be used to determine non-stationary dynamics between two variables which makes it an advantageous choice over the previously described statistical methods. Wavelet analysis was conducted to assess the

relationship between DOC and .(_#), Q and DOC, Q and .(_#), SWC and DOC, and SWC

and .(#).

The majority of traditional mathematical methods that assess periodicities in the frequency domain, such as Fourier Analysis, indirectly assume that the processes are stationary in time.

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Wavelet analysis overcomes this limitation by expanding the time series into time frequency space, transforming the signal into scaled and translated versions of the original wavelet, and thus it is able find localized intermittent periodicities. (Grinsted, et al., 2004; Rathinsamy, et al., 2017). Wavelet transforms can be divided into two classes namely: the continuous wavelet transform (CWT) and the discrete equal (DWT). The DWT displays a compact representation of the data and it is beneficial for noise reduction and data compression. In comparison, the CWT is better for feature extraction purposes. The CWT is therefore beneficial in this project as it is useful in examining two time series together that are expected to be connected in some way.

5.8.1. The Continuous Wavelet Transform (CWT)

According to Grinsted et al. (2004), a wavelet is a function that has zero mean and is localized in both frequency (∆x mk gM,h7lh@ℎ) and time (∆@). The Heisenberg uncertainty principle states that there is always a tradeoff between localization in time and frequency. Grinsted et al. (2004) note that there is a limit to how small the uncertainty product ∆@ ∙ ∆x can be.

The Morlet wavelet is defined as:

Equation 5.4

<0(η) = {)@/!_Q(>#FQ)$%G%

x; = dimensionless frequency

- = dimensionless time

The aim of the CWT is to apply the wavelet as a bandpass filter to the time series. By varying the wavelet’s scale (s), it is stretched in time so that - = n ∙ @, and normalizing it to have unit

energy (Grinsted, et al., 2004). For feature extraction purposes, the Morlet wavelet (with x;=

6) is useful as it delivers a good balance between time and frequency localization. For the Morlet wavelet (with x_; = 6), the Fourier period (>_>+) is almost equal to the scale (>_>+= 1.03 s) (Grinsted, et al., 2004).

The CWT of a time series (Ü_<, , = 1, … , .) with constant time steps ?@, is the convolution of

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Equation 5.5 6_<9_{(n) = à}?@ n â 8<&<; H <&_?@ [(,A_{− ,)}?@ n ]

Practically, it is quicker to implement the convolution in Fourier space where the wavelet power is defined as: | 6_<9_(n)|"_{and the complex argument can be interpreted as the local phase}

(Grinsted, et al., 2004). Since the wavelet is not completely localized in time, the CWT has edge artifacts and thus it is useful to introduce a Cone of Influence (COI). The COI indicates

the area in which the wavelet power caused by discontinuity at the edge has dropped to Q)"_of

the value of the edge and its purpose is to indicate the area in which the edge effects cannot be overlooked.

To assess the statistical significance of wavelet power, it can be related to the null hypothesis

that the signal is created by a stationary process with a stated background power spectrum (0_*).

Multiple geophysical time series have red noise characteristics that can be modelled using first order autoregressive processes (AR1). The Fourier power spectrum of an AR1 process with lag-1 autocorrelation ∝, which has been estimated from the time series conducted by Allen & Smith (1996), is given by:

Equation 5.6

0_* = 1 − ç" |1 − çQ)"(I*_|" ,

é = PmpklQk okQqpQ,!9 l,hQ8

The wavelet transform can be considered as a consecutive series of band-pass filters applied to the selected time series. The wavelet scale is linearly correlated to the characteristic period of the filter (>5+). Therefore, for a stationary process with power spectrum 0* the variance at a

specified wavelet scale, exercising the Fourier convolution theorem, is the variance in the corresponding band of the power spectrum. If the power spectrum is considered smooth, one can approximate the variance at a given scale with 0* by using the é)@= >5+ conversion.

The work of Torrence & Compo (1998) makes use of Monte Carlo methods to indicate that this approximation is useful for the AR1 spectrum. Their paper specifies that the probability

that the wavelet power, of a process with a specified power spectrum (0_*), being greater than

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Equation 5.7

è ê|6<9(n)|"

ë₉" < ií =

1

2 0ìî="(i) ,

where j = 1 for real wavelets and j = 2 for complex wavelets.

5.8.2. The Cross Wavelet Transform (XWT)

The XWT of two time series, 8_<and 9_< , is expressed as 69: _{= 6}9₆:∗_{, where * signifies}

complex conjunction (Grinsted, et al., 2004). The cross wavelet power is defined as |69:_|

and the complex argument arg (69:_{) is understood as the local relative phase between 8}

< and

9_< in time frequency space. Torrence and Compo (1998), state that the theoretical distribution

of the |69:_{| of two time series with background power spectra 0}

*9 and 0*: is as follows: Equation 5.8 è ê|6<9 (n)6<:∗ (n)| ëîëï < ií = :₌(i) j ñ0*K 0*L , :₌ (i) = !m,olhQ,!Q LQjQL Mnnm!lM@Qh 7l@ℎ @ℎQ ikmgMglLl@9 (i)omk M iho

The probability density function (pdf) is expressed as the square root of the product of two ó"

distributions (Grinsted, et al., 2004).

To determine the phase difference between the components of two time series it is necessary to estimate the mean and confidence interval of the phase difference. The circular mean of the phase over areas with more than 5% statistical significance outside the COI can be used to quantify the phase relationship (Grinsted, et al., 2004). The circular mean of a set of angles, M_(, l = 1 … , , is expressed as:

Equation 5.9

M₂ = arg (ó, ô) 7l@ℎ ó = â cos(M₍) M,h ô = â sin(M() ,

<

(?@ <

(?@

It is challenging to determine the confidence interval of the mean angle reliably as the phase angles are dependent. The number of angles used in the calculation can be fixed illogically high by increasing the scale resolution (Grinsted, et al., 2004). Despite this fallback, it is

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interesting to know the scatter of angles around the mean. Thus, the circular standard deviation is defined as: Equation 5.10 n = à−2 ln ö2 ,õ , 7ℎQkQ 2 = t(ó"_{+ ô}"_).

The circular standard deviation varies from zero to infinity and it is consequently analogous to the linear standard deviation. The results are similar to that of the linear standard deviation when the angles are distributed closely to the mean angle (Grinsted, et al., 2004).

5.8.3. Wavelet Transform Coherence (WTC)

The cross wavelet power indicates regions with high common power. In addition to this measure, how coherent the cross wavelet transform is in time frequency space is also useful. Following the work of Torrence & Webster (1999), Grinsted, et al. (2004) has defined the wavelet coherence of two time series as follows:

Equation 5.11 2<"(n) = |3(n)@₆ <9:(n))|" 3(n)@_|6 <9(n)|" . 3 (n)@|6<:(n)|") , 3 = n`mm@ℎl,S miQkM@mk

This equation strongly resembles that of the traditional correlation coefficient, and it is useful to consider the wavelet coherences as a localized correlation coefficient in the time frequency domain (Grinsted, et al., 2004). Grinsted, et al. (2004) define the smoothing operator as follows:

Equation 5.12

3(6) = 3_./'01ú3₊₍₂₁ù6_<(n)ûü ,

3./'01 = n`mm@ℎl,S MLm,S 7MjQLQ@ n!MLQ M8ln

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The smoothing operator should be designed so that it has a similar footprint to that of the wavelet used and consequently, Torrence and Webster (1999) have stated a suitable smoothing operator for the Morlet wavelet:

Equation 5.13 3₊₍₂₁(6)|_. = †6_<(n) ∗ !_@ )+% ".% ° |_. , Equation 5.14 3₊₍₂₁(6)|. = ù6<(n) ∗ !"{(0.6n)û|< , !1 & !2 = ,mk`MLlwM@lm, !m,n@M,@n { = kQ!@M,SLQ op,!@lm,

The factor of 0.6 is the determined scale decorrelation length for the Morlet wavelet (Torrence & Compo, 1998). Monte Carlo methods are used to determine the statistical significance level of the wavelet coherence. A large collective of surrogate data set pairs with the same AR1 coefficients as the input datasets are generated (Grinsted, et al., 2004). The wavelet coherence is then calculated for each pair. This is followed by estimating the significance level of each scale using values outside the COI. Empirical testing conducted by Grinsted, et al. (2004) have indicated that the AR1 coefficients have little influence on the significance level. In contrast to this finding, the specifics of the smoothing operator have a large impact on the significance level. Grinsted, et al. (2004) have stated that for the estimation of the significance level, using Monte Carlo methods, requires of the order of 1000 surrogate data set pairs that the number of scales per octave should be high enough to capture the rectangle shape of the smoothing operator while minimizing processing time. 10 scales per octave were found to be sufficient.

5.8.4. Decoding a WTC plot

Figure 13 provides a key for the interpretation of a WTC plot.

There are some important things to consider when reading a WTC plot:

1. The strength of the correlation can be determined by using the color bar on the right-hand side of the plot. The colour bar ranges from dark blue (2" _{= 0) to dark red (2}" ₌

1). The dark red therefore indicates a perfect correlation and the dark blue indicates no correlation between the two variables at that point in time.